IQIM Postdoctoral and Graduate Student Seminar

Abstract: We study the spreading of initially-local operators under unitary time evolution in a one-dimensional random quantum circuit model which is constrained to conserve a U(1) charge and also the dipole moment of this charge. These constraints are motivated by the quantum dynamics of fracton phases. We discover that charge remains localized at its initial position, providing a crisp example of a non-ergodic dynamical phase of random circuit dynamics. This localization can be understood as a consequence of the return properties of low dimensional random walks, through a mechanism reminiscent of weak localization, but insensitive to dephasing. We further find that the immobile fractonic charge emits non-conserved operators, whose spreading is governed by exponents distinct from those observed in non-fractonic circuits. The entanglement entropy initially grows ballistically, but saturates to an `area law' value, consistent with the lack of thermalization. The non-ergodic phenomenology is found to persist to initial conditions containing non-zero density of dipolar or fractonic charge. Our work implies that low dimensional fracton systems should preserve forever a memory of their initial conditions in local observables under noisy quantum dynamics, thereby constituting ideal memories. It also implies that one and two dimensional fracton systems should realize true many-body localization (MBL) under Hamiltonian dynamics, even in the absence of disorder, with the obstructions to MBL in translation invariant systems and in spatial dimensions greater than one being evaded by the nature of the mechanism responsible for localization. We also suggest a possible route to new non-ergodic phases in high dimensions.